Optics of Wavefront. Austin Roorda, Ph.D. University of Houston College of Optometry

Transcription

1 Optics of Wavefront Austin Roorda, Ph.D. University of Houston College of Optometry

2 Geometrical Optics Relationships between pupil size, refractive error and blur

3 Optics of the eye: Depth of Focus 2 mm 4 mm 6 mm

4 Optics of the eye: Depth of Focus Focused behind retina In focus Focused in front of retina 2 mm 4 mm 6 mm

5 7 mm pupil Bigger blur circle Courtesy of RA Applegate

6 2 mm pupil Smaller blur circle Courtesy of RA Applegate

7 Demonstration Role of Pupil Size and Defocus on Retinal Blur Draw a cross like this one on a page. Hold it so close that is it completely out of focus, then squint. You should see the horizontal line become clear. The line becomes clear because you have used your eyelids to make your effective pupil size smaller, thereby reducing the blur due to defocus on the retina image. Only the horizontal line appears clear because you have only reduced the blur in the horizontal direction.

8 Physical Optics The Wavefront

9 What is the Wavefront? parallel beam = plane wavefront converging beam = spherical wavefront

10 What is the Wavefront? parallel beam = plane wavefront ideal wavefront defocused wavefront

11 What is the Wavefront? parallel beam = plane wavefront ideal wavefront aberrated beam = irregular wavefront

12 What is the Wavefront? diverging beam = spherical wavefront aberrated beam = irregular wavefront ideal wavefront

13 The Wave Aberration

14 What is the Wave Aberration? diverging beam = spherical wavefront wave aberration

15 Wave Aberration: Defocus mm (superior-inferior) Wavefront Aberration mm (right-left)

16 Wave Aberration: Astigmatism mm (superior-inferior) Wavefront Aberration mm (right-left)

17 Wave Aberration: Coma 3 Wavefront Aberration mm (superior-inferior) mm (right-left)

18 Wave Aberration: All Terms mm (superior-inferior) Wavefront Aberration mm (right-left)

19 Zernike Polynomials

20 Wave Aberration Contour Map mm (superior-inferior) mm (right-left)

21 Breakdown of Zernike Terms Zernike term Coefficient value (microns) astig. defocus astig. trefoil coma coma trefoil spherical aberration 2 nd order 3 rd order 4 th order 5 th order

22 Diffraction

23 Diffraction Any deviation of light rays from a rectilinear path which cannot be interpreted as reflection or refraction Sommerfeld, ~ 1894

24 Fraunhofer Diffraction Also called far-field diffraction Occurs when the screen is held far from the aperture. Occurs at the focal point of a lens!

25 Diffraction and Interference diffraction causes light to bend perpendicular to the direction of the diffracting edge interference causes the diffracted light to have peaks and valleys

26 rectangular aperture square aperture

27 circular aperture Airy Disc

28 The Point Spread Function

29 The Point Spread Function, or PSF, is the image that an optical system forms of a point source. The point source is the most fundamental object, and forms the basis for any complex object. The PSF is analogous to the Impulse Response Function in electronics.

30 The Point Spread Function The PSF for a perfect optical system is the Airy disc, which is the Fraunhofer diffraction pattern for a circular pupil. Airy Disc

31 1.22alq = Airy Disk angle subtended at the nodal point wave q

32 As the pupil size gets larger, the Airy disc gets smaller. angle subtended at the nodal point wave PSF Airy Disk radius (minutes) pupil diameter (mm)

33 Point Spread Function vs. Pupil Size 1 mm 2 mm 3 mm 4 mm 5 mm 6 mm 7 mm

34 Small Pupil

35 Larger pupil

36 Point Spread Function vs. Pupil Size Perfect Eye 1 mm 2 mm 3 mm 4 mm 5 mm 6 mm 7 mm

37 Point Spread Function vs. Pupil Size Typical Eye 1 mm 2 mm 3 mm 4 mm pupil images followed by psfs for changing pupil size 5 mm 6 mm 7 mm

38 Demonstration Observe Your Own Point Spread Function

39 Resolution

40 Unresolved point sources Rayleigh resolution limit Resolved

41 As the pupil size gets larger, the Airy disc gets smaller. minmin angle subtended at the nodal point wa PSF Airy Disk radius (minutes) pupil diameter (mm)

42 uncorrected corrected AO image of binary star k-peg on the 3.5-m telescope at the Starfire Optical Range q l = seconds of a 3.5 About 1000 times better than the eye! min = = arc

43 Keck telescope: (10 m reflector) About 4500 times better than the eye!

44 Convolution

45 Convolution (,) (,) (,)PSFxyOxyIxyƒ=

46 Simulated Images 20/20 letters 20/40 letters

47 MTF Modulation Transfer Function

48 low medium high object: 100% contrast image contrast 1 0 spatial frequency

49 The modulation transfer function (MTF) indicates the ability of an optical system to reproduce (transfer) various levels of detail (spatial frequencies) from the object to the image. Its units are the ratio of image contrast over the object contrast as a function of spatial frequency. It is the optical contribution to the contrast sensitivity function (CSF).

50 modulation transfer MTF: Cutoff Frequency 1 mm 2 mm 4 mm 6 mm 8 mm spatial frequency (c/deg) cut-off frequency 57.3cutoffafl= Rule of thumb: cutoff frequency increases by ~30 c/d for each mm increase in pupil size

51 PTF Phase Transfer Function

52 low medium high object image phase shift spatial frequency

53 Relationships Between Wave Aberration, PSF and MTF

54 ()2(,),(,)iWxyiiPSFxyFTPxyepl-Ï =Ì Ó The PSF is the Fourier Transform (FT) of the pupil function The MTF is the amplitude component of the FT of the PSF (){},(,)xyiimtfffamplitudeftpsfxy=è Î The PTF is the phase component of the FT of the PSF (){},(,)xyiiptfffphaseftpsfxy=è Î

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58 Adaptive Optics Flattens the Wave Aberration AO OFF AO ON

59 Conventional Metrics to Define Imagine Quality

60 Root Mean Square Root Mean Square ()()()()()21,, pupil area, wave aberratio

61 Root Mean Square: Advantage of Using Zernikes to Represent the Wavefront ()()()() RMSZZZZ--=+++ astigmatism term defocus term astigmatism term trefoil term

62 diffraction-limited PSF Strehl Ratio Strehl Ratio = eyedlhh H dl actual PSF H eye

63 Modulation Transfer Function contrast /20 20/10 Area under the MTF spatial frequency (c/deg)

64 Other Metrics Volume under the MTF Image Plane Metrics (Strehl ratio) vs Pupil Plane Metrics (eg RMS)

65 Other Optical Factors that Degrade Image Quality

66 Retinal Sampling

67 Sampling by Foveal Cones Projected Image Sampled Image 20/20 letter 5 arc minutes

68 Sampling by Foveal Cones Projected Image Sampled Image 20/5 letter 5 arc minutes

69 Nyquist Sampling Theorem

70 1 Photoreceptor Sampling >> Spatial Frequency I 0 1 I 0 nearly 100% transmitted

71 1 Photoreceptor Sampling = 2 x Spatial Frequency I 0 1 I 0 nearly 100% transmitted

72 1 Photoreceptor Sampling = Spatial Frequency I 0 1 I 0 nothing transmitted

73 Nyquist theorem: The maximum spatial frequency that can be detected is equal to _ of the sampling frequency. foveal cone spacing ~ 120 samples/deg maximum spatial frequency: 60 cycles/deg (20/10 or 6/3 acuity)

74 Thankyou!